Question

prove the identity
\\( \sin ^ { 2 } c ( 1 + \cot ^ { 2 } c ) = 1 \\)
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Explanation:

Step1: Use the Pythagorean identity

We know that \(1+\cot^{2}x = \csc^{2}x\). So, \(\sin^{2}x(1 + \cot^{2}x)=\sin^{2}x\times\csc^{2}x\).

Step2: Use the reciprocal identity

Since \(\csc x=\frac{1}{\sin x}\), then \(\csc^{2}x=\frac{1}{\sin^{2}x}\). So, \(\sin^{2}x\times\csc^{2}x=\sin^{2}x\times\frac{1}{\sin^{2}x}\).

Step3: Simplify the expression

\(\sin^{2}x\times\frac{1}{\sin^{2}x}=1\)

Answer:

1